Z-scores have four very important functions as follows: They divide an acceptabl

Question

Z-scores have four very important functions as follows: They divide an acceptably symmetrical curve into known percentages. They locate individual positions in a distribution very precisely. They locate positions of two or more individuals in the same distribution very precisely one to the other. For mathematical purposes, they provide a common scale for disparate interval and/or ratio measures. As Chief Pilot of a major airline, you are interested in a way to compare pilot performance on an aviation knowledge test. Since there are two different tests that the pilots may take, you want to be able to fairly compare their scores. One of the exams has a score scale from 0 to 150 and another with a score scale of 50 to 300. Describe how you would use z-scores to be able to compare performance of individual pilots.

Explanation / Answer

Answer to the question)
we need to convert the two ratings into normal distribution data

For test one we got

0 to 150 as the rating

Mean M = (0+150)/2 = 75

Standard deviation s = (150-0)/6 = 25

.

for second test , we got

50 to 300 rating scale

thus Mean M = (50+300) / 2 = 175

s = (300-50)/6 = 41.67

.

Now with the help fo these values we can compare the scores of people

For example if a person scores 100 in both the test , its z scores on each of the test can be calcualted as follows

For test 1 , z1 = (100-75)/25 = 1

For test 2 , z2 = (100-175)/41.67 = -1.80

.

Now since the Z score on test 1 1 is greater than z score on test 2 -1.80, thus the performance on test 1 is better as compared to test 2

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